Would it be possible to program an Arduino to flash a set of neon undercarriage lights? If so what must be done? I just was thinking it would be too high voltage for the Arduino.
Totally possible with some appropriately sized relays.
Im no veteran here but i really doubt it can handle the load alone.
Maybe try relays
Do people still use underglow kits these days?
I had one many years ago but now the neons (white) are hung in my outside shed and automatically turn on thanks to a lil door switch.
Any link of what kind of relays I would need?
It depends where you do the switching. If you do it at the supply end then just look at what the supply takes in terms of current and get relays with contacts that will take at least twice that, there is no need to bother about the voltage rating.
If you are switching the output side then you have to ensure that the voltage rating of the contacts is sufficient, the current is so small that any relay will be able to handle it.
Other options could be using an opto isolator Opto-isolator - Wikipedia
if you get one with the correct ratings to switch the output side.
Or a DC Solid state relay for switching the input side.